Genotype by environment interaction and stability analysis for harvest date in sugar beet cultivars

This research assessed the quantitative and qualitative reactions of commercially grown sugar beets to four different harvest dates and their yield stability. The study followed a split-plot design within a randomized complete block design over 3 years. The main plot involved 10 sugar beet cultivars, while the subplot involved four harvest dates: August 13 (HD1), September 7 (HD2), October 3 (HD3), and November 12 (HD4). The study found that environmental conditions, genotypes, and harvest dates significantly affected various traits of sugar beet. Yearly environmental variations and their interactions with genotypes and harvest dates had substantial impacts on all measured traits at the 1% probability level. Additive main effect and multiplicative interaction analysis based on white sugar yield indicated that genotype and environment's additive effects, as well as the genotype–environment interaction, were significant at 1% probability level. Shokoufa and Arya, which exhibit high white sugar yield (WSY) and low first interaction principal component (IPC1) values, are identified as desirable due to their stability across different environments. Among the harvest dates in different years, the fourth and third dates showed a higher yield than the total average. Perfekta and Ekbatan exhibited high specific adaptability. According to the multi-trait stability index, Arta, Arya and Sina were recognized as stable and superior across all measured traits.

filtered through a sieve to obtain a clear liquid, which was then analyzed using the Betalyser device to quantify elements such as SC, N, sodium (Na + ), and potassium (K + ) for the evaluation of sugar beet quality 40 .The resulting values was utilized to estimate WSY, utilizing Eqs.(1) to (3), respectively 41,42 .However, all international, national and institutional guidelines 43 have been taken into account in various stages of experiments.

Statistical analysis
Prior to conducting any analysis, the Grubbs test 44 was utilized to assess the data, assuming normality.Additionally, the Bartlett test 45 was employed to examine the uniformity of experimental error variances across different years.Upon confirming the consistency of these error variances, a combined analysis of variance was executed.This analysis was conducted with a random year effect, while assuming the cultivar and harvest date effects to be fixed.The MTSI was calculated to determine the stability of RY, SC, K + , Na + and N based on Eq. 4 46 .
where MTSI i is the multi-trait stability index of the genotype i, γ ij is the score of the genotype i in the factor j, and γ j is the score of the ideal genotype in the factor j. Scores were calculated based on factor analysis for genotypes and traits.
Due to its incorporation of other studied traits, WSY is deemed a pivotal and ultimate trait.Consequently, an AMMI stability analysis was conducted with regard to this trait.Equation 5, as outlined in the AMMI method 26 , was employed to carry out the stability analysis in 12 environments (2 years and four harvest dates).
where Y ge is the yield of genotype g in environment e; µ is the grand mean; α g is the genotype deviation from the grand mean; β e is the environment deviation; n is the singular value for interaction principal component (IPC n ) and correspondingly 2 n is its eigenvalue; γ gn is the eigenvector value for genotype g and component n; δ en is the eigenvector value for environment e and component n, with both eigenvectors scaled as unit vectors; and ρ ge is the residual.Using the AMMI analysis of variance in SAS software version 9.4 47 , the eigenvalues for each cultivar and environment were calculated.Biplots of this model were drawn to determine the general and specific adaptability of the cultivars.During this investigation, 13 statistics derived from the AMMI model were employed to identify the stable cultivar, through Eqs. ( 6) to (18).
(1) MS = 0.343 K + + Na + + 0.094 alpha amino N − 0.31 where ASTAB is AMMI-based stability parameter 48 , ASI is the AMMI stability index 49 , ASV is the AMMI stability value (where SS IPCA1 is the sum of squares for IPCA 1 , SS IPCA2 is the sum of squares for IPCA 2 , and the IPCA 1 and IPCA 2 scores are the genotype scores in the AMMI model) 50 , AV AMGE is the sum across environments of the absolute value of GEI modeled by AMMI 51 , Da is Annicchiarico's D parameter 52 , D Z is Zhang's D parameter 53 , EV is average of the squared eigenvector values 54 , FA is stability measure based on fitted AMMI model 55 , MASI is modified AMMI stability index 56 , MASV is modified AMMI stability value (where, SSIPC n is the sum of squares of the nth IPC and PC n is the scores of nth IPC) 51 , SIPC is sum of the absolute values of the IPC scores 57 , and Za is the absolute value of the relative contribution of IPCAs to the interaction 51 , WAAS is the weighted average of absolute scores 25 . (

Combined analysis of variance
Variance analysis revealed significant impacts of various factors on the traits measured in this study, including WSY, RY, SC, Na + , K + , and N (Table 3).The results indicated that the year had a significant effect on all traits at the 1% probability level.The main effect of cultivar showed a significant impact on SC at the 5% probability level and K + at the 1% probability level.Furthermore, the interaction between year and cultivar significantly affected all traits at the 1% probability level.The main effect of harvest date was significant for WSY, and RY at the 5% probability level.However, its two-way interaction with the environmental conditions of the year and its three-way interaction involving cultivar and environmental conditions had significant effects on all traits at the 1% probability level.

Stability analysis
The MTSI was employed to comprehensively evaluate experimental genotypes across various independent traits, including RY, SC, Na + , K + , and N, facilitating the identification of desirable cultivars.The factor decomposition was based on PCA, followed by Varimax rotation for result interpretation.Table 4 presents the factor analysis outcomes, selecting factors with eigenvalues greater than one.Each factor's variance is expressed as a percentage, reflecting its significance in explaining overall data variations.Two independent factors accounted for 65.70% of the total data variance in this analysis.The first factor, with an eigenvalue of 1.85, explained 37.10% of the total variance.It exhibited hight negative factor coefficients for SC and N, and a positive coefficient for Na + .The second factor, with an eigenvalue of 1.43 and explaining 28.60% of the variations, included hight negative factor coefficients for RY and K + .The MTSI index for the studied cultivars was calculated based on the factor scores of these two factors.According to this index, a lower MTSI value indicates a closer proximity to the ideal cultivar, while a higher MTSI value suggests a greater distance from the ideal cultivar, making it less desirable.In Fig. 1A, the experimental cultivars are ranked from the highest to the lowest MTSI value.The cultivar with the highest MTSI value is positioned at the center, while the cultivar with the lowest MTSI value is placed in the outermost circle.By applying a 30% selection pressure, the Arta cultivar was ranked first, with Arya and Sina identified as the most ideal cultivars in terms of all traits.Figure 1B highlights the strengths and weaknesses of selected cultivars based on each factor's contribution to the MTSI index.In this diagram, a lower factor share (closer to the outer edge) indicates that  www.nature.com/scientificreports/ the attributes within that factor are nearer to the ideal state.The dashed line represents the theoretical value if all factors contributed equally.Cultivars Sina, Arya, and Arta had the lowest values in the first factor for SC, N, and Na + , which had the highest factor coefficients in this factor, suggesting they are close to the ideal cultivar.
The ideal cultivar is defined by the traits included in each factor and the goals intended to improve those traits.Arta had the lowest share of the second factor, indicating its proximity to the ideal cultivar in terms of RY and K + .In other words, this cultivar exhibits high RY and low K + content.
To enhance the reliability of the experimental analysis and to study interactions between main effects more precisely, the data analysis of WSY was conducted using the AMMI model.The AMMI analysis of variance for WSY demonstrated statistically significant differences between cultivars and environments (additive effects) as well as GEI at the 1% probability level (Table 5).The GEI was further analyzed, yielding the first and second interaction principal components (IPC 1 and IPC 2 ), both of which were found to be significant at the 1% probability level.These components accounted for 60.20% and 15.21% of the sum of squares of the GEI effect, respectively.Combined, IPC 1 and IPC 2 explained 75.41% of the total GEI variance (Table 5).
To consider yield stability and specific adaptation of cultivars to environments, WSY biplots with the IPC 1 (Fig. 2A) and biplots of the first two IPCs (Fig. 2B) were used.According to the biplot of the average WSY against the IPC 1 of the GEI, cultivars with higher WSY (horizontal axis) and lower values (close to zero) in terms of the IPC 1 (vertical axis) are more desirable.Based on this analysis, among the cultivars, Shokoufa and Arya were recognized as the most stable cultivars due to their higher-than-average WSY and the low value of the IPC 1 .Conversely, Ekbatan and Perfekta displayed both high positive and negative values of IPC 1 , suggesting lower stability compared to other studied cultivars (Fig. 2A).The results of environments (year-harvest date) demonstrated that the highest WSY was achieved with HD 4 , followed sequentially by HD 3 and HD 2 , with HD 1 yielding the lowest WSY (Fig. 2A).These results indicate that a delay in the harvesting schedule leads to a substantial increase in WSY.In Fig. 2B, the biplot values of the first and second IPCs for cultivars and environments are displayed.A total of 75.41% of the variation related to the multiplicative effect was explained   Various stability statistics from the AMMI analysis were calculated and are presented in Table 6, along with the average WSY.The average WSY of cultivars across all environments was estimated to be 7.20 t ha −1 .Among the cultivars, Perfecta and Shokoufa exhibited the highest WSY, with 8.84 and 7.92 t ha −1 , respectively.Conversely, the Paya had the lowest WSY, averaging 5.90 t ha −1 .The WSY of Ekbatan, Arta, and Aria were 7.28, 7.18, and 7.38 t ha −1 , respectively, aligning closely with the overall average yield.
The results obtained using several stability statistics-ASTAB, AV AMGE , Da, D Z , EV, FA, and SIPC-indicated that the Arya and Arta, which had the lowest values for these statistics, were the most stable.In contrast, the Ekbatan and Asia, with the highest values for these statistics, were identified as the most unstable.Additional stability statistics, including ASI, ASV, MASI, MASV, Za, and WAAS, also pointed to Motahar and Arya as the  www.nature.com/scientificreports/most stable, given their lowest values in these metrics.Similarly, Ekbatan and Asia were again recognized as the most unstable based on these statistics.Figure 3A and B depicts the convex hull generated by the GGE biplot analysis of sugar beet cultivars across 12 environments, utilizing the IPC 1 and IPC 2 to identify cultivars and environments.The diagram, accounting for 75.33% of the variance in the GEI, illustrates those cultivars closer to a specific environment exhibit specific adaptability, while those nearer to the coordinate origin display general adaptability.The study identified Sina, Arya, and Arta as the most stable due to their proximity to the coordinate origin, while Perfekta, Ekbatan, Paya, and Asia were characterized as the most unstable.
The polygon in the biplot (Fig. 3A) represents the cultivars excelling in specific environments.In this biplot, a polygon is formed by connecting the cultivars that are the furthest from the coordinate origin.The cultivars Asia, Perfecta, Ekbatan, and Paya are positioned at the maximum distances, creating the vertices of the polygon.From the coordinate origin, perpendicular lines are drawn to the sides of this polygon, delineating the megaenvironments 31 .The sections where environments are placed, with cultivars positioned at their vertices, indicate that these cultivars have superior performance in those environments; in other words, they are the best cultivars for cultivation in these specific conditions.Based on this analysis, Perfecta and Shokofa were identified as the best cultivars for all four harvest dates in the second and third years, while Ekbatan was the best cultivar for all four harvest dates in the first year.Cultivars located in sections without any environments are deemed unsuitable for cultivation in any of the tested environments, categorizing them as weak cultivars.The polygonal biplot further grouped the experimental environments into two mega-environments based on WSY.The four harvest dates of the second and third years were clustered into one mega-environment, while the four harvest dates of the first year formed another.This grouping indicates that the environmental conditions of the second and third years are similar to each other, and distinct from those of the first year.
The average environment coordination line (AEC), a diagonal line passing through the biplot's center and the ideal point, indicates that genotypes closer to the circle's center yield higher.Conversely, those further from the perpendicular line to the environmental function's average line are less stable, exerting a more significant impact on interaction.The study highlighted Shokoufa as a cultivar with a higher average WSY and recognized its stability due to its proximity to the ACE line.In contrast, Paya exhibited the most significant distance from the ACE line, indicating weak stability compared to other cultivars (Fig. 3B).

Discussion
The findings from this variance analysis provide profound insights into the multifaceted influences on the quantitative and qualitative traits of sugar beet, encompassing WSY, RY, SC, Na + , K + , and N. The significant effects observed across various factors highlight the intricate interplay between cultivar, environmental conditions, and agronomic practices.The most striking result is the pronounced effect of the year on all measured traits at the 1% probability level.This underscores the critical role that environmental conditions, including climatic variables such as temperature, precipitation, and sunlight, play in determining both the yield and quality of sugar beet crops.The significant year-to-year variability in these conditions suggests that any agricultural practice or cultivar designed to optimize sugar beet production must be adaptable to fluctuating environmental conditions.This finding aligns with previous studies that have highlighted the importance of weather patterns and climate change on crop performance.The cultivar's main effect was significant for SC at the 5% and K + at the 1% probability level.This indicates that genetic factors are crucial for specific traits related to sugar quality.The significant interaction between year and cultivar at the 1% probability level for all traits further emphasizes that while cultivar has a foundational impact, its expression can be profoundly modified by environmental conditions.This interaction suggests that breeding programs should focus on developing cultivars that are not only high-performing under optimal conditions but also resilient to environmental variations.
The effect of the harvest date on WSY and RY at the 5% probability level reveals that the timing of harvest is a critical agronomic practice that can influence productivity.The significant two-way interaction between harvest date and environmental conditions, as well as the three-way interaction involving cultivar, environmental conditions, and harvest date, at the 1% probability level, highlights the complexity of optimizing harvest time.These interactions suggest that the ideal harvest date may vary depending on both the specific cultivar and the prevailing environmental conditions of the year.Therefore, dynamic harvest strategies that can be adjusted based on real-time environmental monitoring may be necessary to maximize yield and quality.For breeders, these findings suggest a dual focus on genetic improvement and environmental adaptation.Future breeding programs might benefit from incorporating traits that confer stability under diverse environmental conditions.Moreover, the development of predictive models that integrate genotype performance with environmental data could facilitate better decision-making in crop management.Based on the obtained results from the experiment conducted by Sadeghzadeh Hemayati et al. 58 the environment and its interaction with the genetic structure of different genotypes played a significant role in the phenotypic expression of WSY in sugar beet genotypes.This resulted in different responses in terms of WSY based on the conditions of different environments.Similarly, the study conducted by Saremirad and Taleghani 38 indicated that GEI outweighs the quantitative and qualitative characteristics of sugar yield in sugar beet hybrids.Therefore, this interaction should be considered when breeding new hybrids, as it allows for decisions regarding breeding for general or specific adaptation, depending on the yield stability in different environmental conditions.In order to better understand and reveal the GEI, multivariate statistical methods can be more useful.These methods can provide insights into the complex relationships between genotypes and environments, allowing for a more comprehensive understanding of the factors influencing crop yield and the development of cultivars with stability and adaptability to target environments 35 .
The application of the MTSI offers a robust framework for evaluating the overall performance of sugar beet cultivars across multiple traits.By integrating various independent traits such as RY, SC, Na + , K + , and N, the MTSI index facilitates a holistic assessment of cultivars.This comprehensive evaluation is essential for breeding programs focused on improving multiple quantitative and qualitative traits simultaneously.In fact, its comprehensive approach facilitates the identification of top-performing cultivars, as demonstrated by the selection of Arta, Arya, and Sina in this study.
The effectiveness of the MTSI index is further validated by its successful application in previous studies across different crops and conditions.Sharifi et al. 59 use of the MTSI index in rice genotypes to identify superior genotypes based on yield and stability highlights its versatility.Similarly, Rajabi et al. 60 application of the MTSI index in identifying stable sugar beet genotypes under rhizomania disease conditions demonstrates its relevance in stress environments.Taleghani et al. 39 study, which used the MTSI index to identify genotypes with desirable traits such as RY, WSY, SC, and ECS, further corroborates its efficacy.The findings of these studies align with the results obtained in this research, demonstrating the effectiveness of the MTSI index in identifying superior genotypes.
The findings from the AMMI model analysis provide a comprehensive understanding of the interactions between cultivars and environments concerning WSY.The significant additive effects of cultivars and environments indicate that both genetic makeup and environmental conditions independently contribute to variations in WSY.However, the significant multiplicative effects (GEI) reveal that the interaction between cultivar and environment is also crucial.AMMI model indicated that the GEI was significant and 2.77 times larger than the cultivar effect.This finding is consistent with several studies that have recorded a significant GEI effect in sugar beet field trials 16,[35][36][37]39,61 . Envirnmental variables such as temperature, solar radiation, precipitation, and soil properties play a crucial role in determining where and how plants grow 38,62 .Weather conditions during the trial varied significantly, with extreme drought and exceptionally high temperatures observed in the first year, while the second and third years experienced adequate rainfall and good distribution.The study noted that the absence of rainfall and lower temperatures in April of the first year resulted in fewer plants per unit area.An important reason for the GEI is likely due to source limitation in most growth phases of sugar beet 12 .This finding is important for breeders and farmers as it suggests that selecting genotypes solely based on their average performance might not be sufficient; instead, their performance stability across various environments should also be considered.
The use of biplots to visualize the interaction effects provides practical insights into the stability and adaptability of different sugar beet cultivars.Cultivars like Shokoufa and Arya, which exhibit high WSY and low IPC 1 values, are identified as desirable due to their stability across different environments.This makes them suitable candidates for regions with variable growing conditions.On the other hand, cultivars such as Ekbatan and Perfekta, with high IPC 1 values, demonstrate greater sensitivity to environmental variations, indicating lower stability.This information is crucial for breeding programs aimed at developing robust cultivars that can withstand environmental variability.Ebmeyer et al. 34  www.nature.com/scientificreports/ 2 years.They found significant effects of GEI on RY and SC.In addition, they indicated that high yield potential did not ensure sustainable high yields.
As can be seen in Fig. 2A across all 3 years of the experiment, the highest WSY was obtained from late harvest dates.The highest WSY was recorded by HD 4 in the first year and HD 3 in the second year.In the third year, the highest WSY was obtained from HD 4 .The study recommended harvesting on either HD 4 or HD 3 to achieve the highest WSY, as these times were found to be ideal for maximizing WSY.The higher WSY and its components in HD 4 and HD 3 were attributed to their longer growth period, better utilization of environmental factors such as light, temperature, and humidity, and synchronization of growth stages with favorable environmental conditions.Previous research has suggested that shortening the growth period reduces WSC and subsequently decreases RY 63 .Other investigations have also indicated the potential benefits of delaying root harvest for sugar beet cultivation 14,16,64,65 .
The identification of cultivars such as Aria and Motahar, which are close to the origin in the biplot of the first and second IPCs, indicates their general adaptability.These cultivars show less fluctuation in yield across different years and harvest dates, making them reliable choices for consistent production.The ability to identify such generally adaptable cultivars is vital for ensuring stable agricultural output in the face of changing climatic conditions.
The AMMI model's stability statistics-ASTAB, AVAMGE, DA, DZ, EV, FA, and SIPC-are pivotal in determining the stability of cultivars.Arya and Arta, which had the lowest values for these statistics, emerged as the most stable cultivars.Their low values indicate minimal interaction with environmental variables, making them reliable choices for diverse growing conditions.Conversely, Ekbatan and Asia, with the highest values, were identified as the most unstable cultivars, implying significant GEIs and less predictable performance.Further stability metrics, including ASI, ASV, MASI, MASV, Za, and WAAS, corroborated the findings of AMMI model.Motahar and Arya's low values in these metrics reinforced their status as the most stable cultivars.The consistency of Arya across multiple stability metrics underscores its robustness and adaptability.Once again, Ekbatan and Asia were identified as the least stable, highlighting their susceptibility to environmental variability.
The identification of stable cultivars like Arya and Arta is particularly valuable for breeding programs.These cultivars can serve as foundational genotypes for developing new cultivars that combine high yield with stability.The dual focus on yield performance and stability ensures that the resulting cultivars are not only productive but also resilient to environmental fluctuations.The findings suggest that incorporating stability metrics into the selection criteria can significantly enhance the effectiveness of breeding programs.

Conclusion
In the spring cultivation of sugar beet, delaying the harvest can increase WSY, but it may also hinder timely field preparation for the next crop due to autumn rains.Therefore, identifying the optimal harvest dates is crucial to maximize economic yield and ensure adequate time for land preparation.This research found that the highest WSY was achieved with harvest dates HD 4 and HD 3 .However, harvesting on HD 3 is recommended to balance yield and field preparation time.Selecting the genotype with the highest WSY would be advantageous across all harvest dates, allowing for efficient selection during the first harvest and reducing time and costs.Notably, Perfekta demonstrated the highest WSY over 3 years, followed by Shokoufa.When assessing cultivar stability based on WSY, Arta and Arya showed high general stability, while Perfekta and Ekbatan exhibited high specific stability.Furthermore, the MTSI identified Arta, Arya, and Sina as the most stable cultivars.These cultivars emerged as the top-ranking cultivars, suggesting them as a potential candidate for further breeding programs.

Figure 1 .
Figure 1.Ranking of cultivars in ascending order based on the multitrait stability index (A) and strengths and weaknesses of selected cultivars as the ratio of each factor in the calculated multitrait stability index (B).
by this biplot.According to this biplot, cultivars close to the origin of the coordinates have general adaptability.As seen in the figure, Arya and Motahar are generally adaptable due to their proximity to the origin of the coordinates, indicating less yield fluctuation across different years and harvest dates.

Figure 2 .
Figure 2. Scatter plot illustrating the relationship between cultivars and environments, using the mean white sugar yield and the first (A) and second (B) principal components.FY first year, SY second year, TY third year, HD 1 harvest dates on August 13, HD 2 harvest dates on September 7, HD 3 harvest dates on October 3, HD 4 Harvest dates on October November 12.

Figure 3 .
Figure 3. (A) Polygon generated through the GGE biplot method to identify optimal cultivars for each environment, and (B) Ranking of cultivars based on average white sugar yield and stability.FY first year, SY second year, TY third year, HD 1 harvest dates on August 13, HD 2 harvest dates on September 7, HD 3 harvest dates on October 3, HD 4 Harvest dates on October November 12. (B) The red axis featuring an arrow and intersecting the coordinate origin symbolizes stability (AEC), while the red axis marked solely by a line denotes the average yield of the genotypes.

Table 2 .
The average temperatures and rainfall data recorded at the research stations for the years 2019, 2020, and 2021.

Table 5 .
Analysis of variance of white sugar yield in sugar beet cultivars using the AMMI Model in Karaj (2019-2021).

Table 6 .
Mean white sugar yield and various AMMI stability parameters for sugar beet cultivars across 12 environments in Karaj (2019-2021).ASTAB AMMI-based stability parameter, ASI AMMI stability index, ASV AMMI stability value, AV AMGE sum across environments of the absolute value of GEI modeled by AMMI, Da Annicchiarico's D parameter, D Z Zhang's D parameter, EV average of the squared eigenvector values, FA stability measure based on fitted AMMI model, MASI modified AMMI stability index, MASV modified AMMI stability value, SIPC sum of the absolute values of the IPC scores, Za absolute value of the relative contribution of IPCs to the interaction, WAAS weighted average of absolute scores.